Unification Theories: Means and Generalized Euler Formulas

Iordanescu, Radu; Nichita, Florin F.; Pasarescu, Ovidiu

doi:10.3390/axioms9040144

Cited by 7 publications

(9 citation statements)

References 14 publications

(17 reference statements)

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“…The Yang-Baxter equation is an important tool for the theory of quantum groups, knot theory, the theory of universal quantum gates, and the theory of quantum computers (see [49][50][51][52][53][54][55]).…”

Section: The Yang-baxter Equationsmentioning

confidence: 99%

Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

et al. 2021

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The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain. As a mathematical model, we propose topoi and their non-standard enlargements as models, due to the fact that their logic corresponds well to human thinking. For this reason, we built non-standard analysis in a special class of topoi; before now, this existed only in the topos of sets (A. Robinson). Then, we arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory (IIST); a class of models for it is provided, namely, non-standard enlargements of the previous topoi. We also consider the genetic–epigenetic interplay with a mathematical introduction consisting of a study of the Yang–Baxter equations with new mathematical results.

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Section: The Yang-baxter Equationsmentioning

confidence: 99%

Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

et al. 2021

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“…In the next section, we present the colored Yang-Baxter equation. We propose the problem of finding algorithms for solving the system of Equations ( 5)- (9). Solutions for that system will lead to new solutions for a spectral-dependent Yang-Baxter equation.…”

Section: Introductionmentioning

confidence: 99%

On the Colored and the Set-Theoretical Yang–Baxter Equations

Iantovics

Nichita

2021

Axioms

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This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied.

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“…Setting n = 0, we have B (0) k (y) = y n . Putting y = 0, we have the Bernoulli numbers of order n: B [1,3,5,6,11,15,16,[18][19][20][21][22][23][24]). A relation between the numbers θ n − → x v , − → y v and the numbers B…”

Section: Introductionmentioning

confidence: 99%

New Families of Special Polynomial Identities Based upon Combinatorial Sums Related to p-Adic Integrals

Şimşek

2021

Symmetry

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The aim of this paper is to study and investigate generating-type functions, which have been recently constructed by the author, with the aid of the Euler’s identity, combinatorial sums, and p-adic integrals. Using these generating functions with their functional equation, we derive various interesting combinatorial sums and identities including new families of numbers and polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, the Changhee numbers, and other numbers and polynomials. Moreover, we present some revealing remarks and comments on the results of this paper.

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Unification Theories: Means and Generalized Euler Formulas

Cited by 7 publications

References 14 publications

Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

On the Colored and the Set-Theoretical Yang–Baxter Equations

New Families of Special Polynomial Identities Based upon Combinatorial Sums Related to p-Adic Integrals

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